The present invention relates to an optimized process control method and apparatus therefor.
In the series of steps for the planning, designing, construction and operation of an apparatus or system, it is very important to obtain a maximum profit or to reduce the overall cost to the minimum in every case, which is generally called "the optimization problem" in the art. Process control is directly related with the operation of an apparatus so that it is an object of optimization.
In the case of the optimization of process control, the operational conditions to attain maximum profit are obtained based on variables such as rate of feed of a material or fuel and so on, temperature, pressure, etc., and these operational condition values are determined as set values of the control loops.
In order to optimize a process, it is a rule of thumb to understand and model the object process. In practice, in process control, the object systems which must be optimized are almost always of nonlinear characteristics. Moreover, the problem to be solved will be a nonlinear planning problem of the order of n, where n is the number of variables.
FIG. 1 is a block diagram illustrating a conventional system to be optimized.
This system is equipped with a control loop controller group 4 in order to apply manipulated values (MV) such as the degree of opening of valves, the electric power to be supplied and so on, to a real process 5 such as a plant or the like and also to derive process values (PV) representative of temperatures, flow rates and so on. The controller group 4 is connected to an optimization algorithm device 21 and a process model device 20 which constitute an optimized control device. The optimization algorithm device 21 is a kind of an arithmetic unit used to attain various arithmetic operations in order to attain a maximum optimization and outputs the results or set values (SV) so as to cause the controller group 4 to deliver the manipulated values (MV) to the real process 5. The process model device 20 is a component part in which a process model is stored and it applies the process values (PV) received from the controller group 4 to the process model equations.
The optimization algorithm device 21 delivers manipulated variables 23 to the process model device 20 and obtains the evaluation functions 22 which are representative of optimized operational conditions which are obtained by the process model device 20. The evaluation functions 22 are solved and the optimum variables are delivered to their respective control loops 4.
When there are n variables and the evaluation function is expressed as f(x.sub.1, x.sub.2, . . . , and x.sub.n), the process for obtaining the value of each variable at which the evaluation function f has a maximum or minimum value is the optimization problem. In order to solve this problem, it suffices to obtain a differential coefficient of the evaluation function f, but in general this cannot be obtained by analytic methods.
Meanwhile in the case of the optimum control of a control system of a plant which is so complicated in its physical and chemical behaviors that it is difficult to make a realistic model, in general, few computers have been able to incorporate practical process model equations.
As one example of the optimized control systems, a kraft recovery boiler combustion control system in the paper and pulp industry may be considered. In this system, the kraft recovery boiler has the double function of generating steam as in the case of other general boilers and recovering the chemical agents added, during the process of crushing tips with steam.
The fuel for the kraft recovery boiler is a waste liquid called black liquor obtained in the process of steam digesting of tips. Black liquor contains not only inflammable organic components included in the tips, but also the chemical agents (soda) added in the process of steam digesting the tips. Inflammable organic components are burned and the heat obtained by this combustion is derived in the form of steam. The chemical agent is contained in black liquid in the form of Glauber's salt (Sodium Sulfate: Na.sub.2 SO.sub.4). Because of the reduction reaction, it becomes smelt (sodium sulfide: Na.sub.2 S) and is recovered from the bottom of the furnace in the form of a liquid. It follows therefore that in order to recover the chemical agents, the deoxidation atmosphere for causing such a reduction reaction must be formed. In order to form such an atmosphere within the furnace, it is required to form the semi-dried deposite of black liquor called a char bed, which in turn must be burned. Black liquor sprayed into the furnace drops while its water content is derived by radiant heat resulting from the combustion so that the char bed is formed at the bottom of the furnace. The combustion air is blown into each stage within the furnace in such a way that it surrounds the char bed.
Unlike general boilers, two of the most important objects in the optimized combustion control of the recovery boiler are (1) not only to increase the thermal efficiency of the boiler (2) but also to increase the recovery rate of the chemical agent; that is, to increase the degree of reduction of smelt. Furthermore, in order to prevent atmospheric pollution, the discharge of SO.sub.x, NO.sub.x, TRS (Total Reduction Sulphur) and so on must be reduced to a minimum.
The manipulated variable in the optimum combustion control of the kraft recovery boiler is the combustion air which is blown into the bottom of the char bed and over its surface and the space above it.
In the case of optimum control for the kraft recovery boiler, a suitable quantity of air must be distributed and blown into the furnace. In order to realize such optimum control, the model equations of the object process must be preferably defined as described above. However, unlike the general boilers, the chemical reactions and physical behaviors in the furnace of the recovery boiler are extremely complex so that it is almost impossible to analyze the above-mentioned phenomena and to define a practical model.
In this case, the process model device 20 shown in FIG. 1 is eliminated as shown in FIG. 2 and the process itself is assumed to include a process model in the form of a black box, thereby searching for an optimum point. That is, the determination of an optimum point is carried out in such a way that the manipulated values 10 are directly varied depending upon set values (SV) 9 and in accordance with an optimization algorithm so as to interfere the process. In this case, the evaluation function for determining an optimum point is directly obtained using the process values (PV) 11 in the plant which is in the form of a feedback value of the manipulated variables.
That is, the air amounts charged into three different portions in the furnace, which are the manipulated variables, are varied in accordance with an optimization algorithm so as to determine an optimum point in a trial and error manner. As a result, an optimum point can be determined without directly interfering with the process. In this case, the evaluation function required for the determination of an optimum point is computed from process values (PV). For instance, both of the steam generating efficiency and the additive agent recovery rate are taken into consideration so that the nonlinear combined equation of the boiler efficiency, the temperature of the surface of the char bed and the analyzed value of the concentration of the exhaust gas is used as an evaluation function. As an optimization algorithm for determining an optimum point in a trial and error manner, a nonlinear simplex method, a complex method which is a modification of the nonlinear complex method so that the modified complex method can be utilized even when certain limited conditions exist, other modifications of the nonlinear simplex method or the like may be used. Of these methods the simplex method has been widely used.
According to the simplex method, a simplex which is an initial value consisting of (n+1) points geometrically arranged on R.sup.n (n-dimension) is first generated and at each point, the value of the evaluation function f (x.sub.1, x.sub.2, . . . , and x.sub.n) is compared so that in response to the result of the comparison, the simplex is moved by one point every one fundamental operation, thereby approaching a point at which the evaluation function has a minimum value.
According to this method, need not to obtain a differential coefficient so that the method can be applied to a case in which correct model equations of the process cannot be defined. As a result, this method has a feature that the optimum control can be carried out with a high degree of accuracy.
However, in the case of the method in which the real process is directly utilized so as to search for and determine an optimum point, the operation continues even from the time when the search is started to the time when an optimum point is determined (search is converged), the optimum operation is not carried out during that interval. As a result, according to such trial and error searching method, the process may be carried out at a point in the vicinity of the worst point even for a short time interval. As a consequence, there arises the problem that pollutants are discharged.
The evaluation function which is an important element in the search and determination of the optimum point is computed on the basis of the process values (PV) including external disturbances exerted upon the process. Especially in the case of the kraft recovery boiler of the type described above, variations in the composition of black liquor between lots of pulp materials and external disturbances such as the adhesion of hume to the furnace wall occur very frequently. Therefore because of a sudden disturbance, the process is adversely affected temporarily so that an evaluation function which is useless is obtained. Consequently, the optimum point search and determination process is delayed. Furthermore, even after an optimum point is defined, the optimum point search and determination process is resumed due to the external disturbances.
Moreover, in the case of defining an optimum point by using the simplex method and in the case of a simplex consisting of a plurality of points, since the simplex moves only to one vertex point in each fundamental operation that when there exist many variables, the movement of the simplex is low and the determination of an optimum point is delayed. As a result, there arises the problem that a long period of time from the starting of the search to converge is required so that the operation is adversely affected.